# Synthetic Potential Outcomes and Causal Mixture Identifiability

arXiv: https://arxiv.org/abs/2405.19225 · HTML: https://mlsanity.com/paper/2405.19225/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 52 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 20 of 20)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Comment on "Blessings of Multiple Causes"](https://mlsanity.com/paper/1910.05438/) (2019)
- [A Selective Review of Negative Control Methods in Epidemiology](https://mlsanity.com/paper/2009.05641/) (2020)
- [Causal Imputation via Synthetic Interventions](https://mlsanity.com/paper/2011.03127/) (2020)
- [Source Identification for Mixtures of Product Distributions](https://mlsanity.com/paper/2012.14540/) (2020)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [Counterexamples to "The Blessings of Multiple Causes" by Wang and Blei](https://mlsanity.com/paper/2001.06555/) (2020)
- [The Sparse Hausdorff Moment Problem, with Application to Topic Models](https://mlsanity.com/paper/2007.08101/) (2020)
- [Double Negative Control Inference in Test-Negative Design Studies of Vaccine Effectiveness](https://mlsanity.com/paper/2203.12509/) (2022)
- [Identification of Mixtures of Discrete Product Distributions in Near-Optimal Sample and Time Complexity](https://mlsanity.com/paper/2309.13993/) (2023)
- [Causaltoolbox---Estimator Stability for Heterogeneous Treatment Effects](https://mlsanity.com/paper/1811.02833/) (2018)

## Built on by (most cited first, 3 of 3)

- [Estimating Aleatoric Uncertainty in the Causal Treatment Effect](https://mlsanity.com/paper/2602.08461/) (2026)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)
- [Masking Causality and Conditional Dependence](https://mlsanity.com/paper/2603.06984/) (2026)

## Abstract (arXiv)

Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by grouping populations according to different notions of similarity. This paper proposes grouping with respect to the causal response of an intervention or perturbation on the system. This definition is distinct from previous notions, such as similar covariate values (e.g. clustering) or similar correlations between covariates (e.g. Gaussian mixture models). To solve the problem, we ``synthetically sample'' from a counterfactual distribution using higher-order multi-linear moments of the observable data. To understand how these ``causal mixtures'' fit in with more classical notions, we develop a hierarchy of mixture identifiability.